In seismic surveys, a seismic source is actuated to induce seismic waves at or near the surface of the earth. Explosive sources, vibrating devices and airguns are examples of seismic sources. The seismic waves propagate into and through the earth and are reflected, refracted, and diffracted by geological formations within the earth. Some seismic waves are directed back to the earth's surface, and can be detected by a plurality of seismic receivers (or seismic sensors), such as geophones or hydrophones, deployed at the earth's surface. Each such receiver monitors and records the seismic wavefield at the receiver's location. Typically a receiver monitors the seismic wavefield for a given period after actuation of a seismic source. The data received and recorded by a receiver are in the form of a record of the variation over time of one or more components of the seismic wavefield, and are collectively called a trace. The collection of traces is stored for further processing in known ways to obtain information about the earth's subsurface. Such information is commonly interpreted by geophysicists to detect the possible presence of hydrocarbons, or to monitor changes in hydrocarbon bearing rocks in the subsurface.
Seismic data in general contains noise signals, which may be coherent or incoherent, as well as the desired seismic reflection signals. These noise signals, hereafter referred as just “noise”, interfere with the interpretation of the seismic signals, and degrade the quality of the subsurface images that can be obtained by processing the recorded seismic data. It is therefore very desirable to suppress or attenuate the noise that is present in the recorded seismic data before processing the data to obtain an image of the earth's interior.
In land-based seismic surveys, source-generated coherent noise such as ground-roll waves and air-waves are the dominant noise types, and can lead to severe degradation in the quality of the processed data. In marine seismic surveys, energy propagating as waves trapped in the water-column or in the near-surface layers of the seabed is a significant source of coherent noise. Further significant sources of coherent noise are swell noise and bulge-wave noise, which result from waves propagating down the streamers on which the receivers are mounted. Other sources of coherent noise in marine seismic surveys include passing vessels, other vessels acquiring seismic data in the vicinity, and nearby drilling rig activity.
One conventional method of noise attenuation in seismic acquisition is through the process of analogue group-forming. The receivers are hard-wired into groups, or “arrays” of receivers. The analogue output of an array is the normalised sum (arithmetic average) of all traces, acquired by the receivers in the array. The array support is usually rectangular. Consequently, the spectral response of the array is approximately a frequency-independent 2-D sinc function in the wavenumber (kx-ky) space. However, since ground-roll waves have finite apparent velocity, a frequency independent filter is not ideal for separating signal and noise in acquired seismic data. High frequency components of some seismic events (for example seismic events arising from dipped, non-horizontal reflectors) may be erroneously attenuated, while the low frequency components of the ground-roll noise may not be attenuated.
Recently, point receiver recording (also known as single sensor acquisition) of seismic data has become possible. In point receiver recording the receivers are not hard-wired into groups, so that the individual data traces recorded by each receiver are recorded and are available for processing. While it is still desirable to sum traces acquired by more than one receiver, the summation is performed at the processing stage by digital group-forming on individual traces from many receivers. Point receiver recording allows the use of digital group-forming for better noise attenuation and signal preservation. It is also possible to vary the size and composition of the groups formed in the digital group-forming process.
Digital group-forming consists of the application of a 3-D filter with two spatial axes and one temporal frequency axis, which allows much better control of the signal protection and noise rejection zones in the spectral (frequency-wavenumber—f-kx-ky) domain. The 3-D filter may be either deterministic as described for example in the co-owned British patent application no. 0400409.9, or adaptive as described for example in the co-owned published international patent applications Wo 99/60423 and WO 97/25632 or, in fact, any other known method to define a suitable filter.
The natural data structures of the data input into the group-forming process are individual common source gathers. A common source gather is, as the name suggests, the ensemble of all point receiver recordings acquired following actuation of an individual seismic source. In the digital group-forming process a digital group-forming (DGF) filter is convolved with the point receiver data traces, and the output is a set of digital group-formed traces. Usually, the number of output traces will be far less than the number of original point receiver traces.
The design of multi-dimensional filters used for digital group-forming conventionally requires regular sampling of the seismic data. Regular sampling in the context of this invention means for example spatial sampling of seismic data at locations arranged on a regular grid such as a rectangular or a hexagonal grid, although other regular grid patterns can be used as well. The sampling along the time axis is also required to be regular.
One problem encountered in processing seismic data is that, in a real seismic survey, the seismic wavefield is often sampled at locations that are spatially irregular and do not lie on a regular grid. Seismic data is therefore available only for points that are irregularly distributed. Points for which seismic data are available are hereinafter known as “data points”.
The fact that data points are not regularly distributed is usually ignored in the design and application of multi-dimensional filters for group-forming. Consequently, the actual response of the DGF filter can be different from the theoretical response of the filter. The signal pass zone of the filter in the spectral domain can be distorted, so that the pass zone may be smaller than designed, the gain may end up being significantly different from unity, and the phase may end up being significantly different from zero. The side-lobes of the filter (i.e. the gain in the reject zone) may be significantly increased. This can lead to distortion of the seismic signal and to noise leakage.
Newman and Mahoney have studied, in “Geophysical Prospecting”, Vol. 21, pp.197-219 (1973), the effects of errors in sensor positions in 1-D linear arrays, and have shown that the side-lobes in the array reject regions when sensor positions are not regular are much higher than the theoretical values corresponding to the perfect arrays. The inventors have made similar calculations for 2-D and 3-D arrays, using both conventional analogue groups as well as those designed using APOCS, and these calculations have confirmed the previous 1-D results.
A. J. W. Duijndam et al. have suggested, in “Irregular and Sparse Sampling in Exploration Seismology”, in Nonuniform Sampling: Theory and Practice, ed. F. Marvasti, Kluwer Academic , pp. 479-517, New York (2001), that one way to overcome the problem of multi-dimensional filtering of irregularly sampled seismic data would be to regularise the irregularly sampled seismic data, by interpolating the data to a common regular sampling pattern, and then to apply filters designed for that regular pattern. While this approach would in principle be effective, this approach would generally not be practicable in the case of a real seismic survey. Applying this method to the data acquired in a practical seismic survey would require vast computing time and would be too expensive, given the enormous size of 3-D seismic data sets.
Another limitation of this prior art approach is that the regularisation approaches have to assume that the data is bandlimited in the wavenumber domain. In practice, the spatial bandwidth of some types of coherent noise, in particular ground-roll noise, may change depending on the receiver location, and be difficult to estimate beforehand.